At a moment when fashion designers increasingly steal the flashbulbs for themselves, Katayone Adeli is a rare designer who has survived--and thrived--on word of mouth alone. She does no advertising for her line, holds no runway shows and shuns the press and the party circuit. Yet last year her 2 1/2-year-old label did $20 million in sales and netted her a nomination for the Perry Ellis Award for new...